On the unicity of braidings of quasitriangular Lie bialgebras

Abstract

Any quantization of a quasitriangular Lie bialgebra g gives rise to a braiding of the dual Poisson-Lie formal group G^*. We show that this braiding always coincides with the Weinstein-Xu braiding. We also define the lifts of the classical r-matrix r as certain functions on G^* x G^*, prove their existence and uniqueness using co-Hochschild cohomology arguments and show that the lift can be expressed in terms of r by universal formulas.

References in corpus (3)

• Quantization of Lie bialgebras, V
• Tressages des groupe de Poisson formels à dual quasitriangulaire
• Braiding structures on formal Poisson groups and classical solutions of the QYBE

Cited by in corpus (2)

• Braiding structures on formal Poisson groups and classical solutions of the QYBE
• A cohomological construction of quantization functors of Lie bialgebras